Selective Linear or Quadratic Optomechanical Coupling via Measurement

Michael R Vanner

doi:10.1103/physrevx.1.021011

Abstract

The ability to engineer both linear and non-linear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical displacement coupling can be achieved using the optomechanical interaction linearly proportional to the mechanical position. The resulting square displacement measurement strength is compared to that attainable in the dispersive case using the direct interaction to the mechanical displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.

Highlights

The main approaches to cavity optomechanics [1] can be divided into two categories—reflective and dispersive
Displacement-squared measurements have so far been predominantly considered in dispersive optomechanics; the optimal square-displacement measurement strength obtained in the scheme introduced here can be significantly stronger than that available in dispersive optomechanics as it scales more favorably with the cavity finesse
This opens the possibility that optomechanics with an interaction Hamiltonian that is linear with the mechanical position may provide a route to observe mechanical-energy quantization, as was considered in [2]

Summary

INTRODUCTION

The main approaches to cavity optomechanics [1] can be divided into two categories—reflective and dispersive. The second approach is depicted, where a mechanical element is positioned within an optical field and partial reflection from both sides gives rise to a dispersive interaction In this arrangement, the cavity frequency varies periodically with mechanical displacement. Of particular interest here, measurement of the amplitude quadrature may give outcomes that could have resulted from two distinct mechanical positions This is due to an effective displacement-squared coupling, which can be used for non-Gaussian state preparation. Homodyne detection of the amplitude quadrature has the outcome probability density PrðÁQXÞ 1⁄4 TrMðÇyXÇXiMn Þ, where ÇX is the corresponding measurement operator In this pulsed regime ÁQX has mechanical dependence only on XM, which allows ÇyXÇX to be interpreted as an outcome probability density conditioned on a mechanical position. Whpeffirffiffie the mean momentum transfer is lin 1⁄4 ð5 2=3ÞNpglin=

COMPARISON TO THE DISPERSIVE QUADRATIC INTERACTION

EXPERIMENTAL PROTOCOL AND DISCUSSION

Findings

CONCLUSION